Cluster soft sets and cluster soft topologies

The cluster soft point is an attempt to introduce a novel generalization of the soft closure point and the soft limit point. A cluster soft set is defined to be the system of all cluster soft points of a soft set. Then the fundamental properties of cluster soft sets are demonstrated. Moreover, the concept of a cluster soft topology on a universal set is introduced with regard to the cluster soft sets. The cluster soft topology is derived from a soft topology with an associated soft ideal, but it is finer than the original soft topology. On the other hand, if we start constructing the cluster soft topology from another cluster soft topology, we will end up with the first cluster soft topology we started with. The implication of cluster soft topologies is highlighted using some examples. Eventually, we represent the cluster soft closed sets in terms of several forms of soft sets

SOFT CONNECTED PROPERTIES AND IRRESOLUTE SOFT FUNCTIONS BASED ON B-OPEN SOFT SETS

In this paper, we introduce another application on the b-open soft sets [10], by studying the notion of connectedness based on it. We give basic definitions and theorems about it. Further, we introduce the notion of b-irresolute soft functions as a generalization of the b-continuous soft functions and study their properties in detail. Finally, we show that the surjective b-irresolute soft image of soft b-connected space is also soft b-connected